Finite Group Databasebeta

← #6477086

Subgroups — #6477086

Order 512.

1944 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2851C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic
3#33151C212yesmaximal, complemented
4#32960C212yesmaximal, complemented
5#30170C214yesmaximal, complemented
6#29298C212yesmaximal, complemented
7#29106C212yesmaximal, complemented
8#27653C212yesmaximal, complemented
9#27601C211yesmaximal, characteristic
10#27600C211yesmaximal, characteristic
11#24705C214yesmaximal, complemented
12#24307C212yesmaximal, complemented
13#24006C211yesmaximal, characteristic
14#24003C211yesmaximal, characteristic
15#22079C212yesmaximal, complemented
16#22078C212yesmaximal, complemented
17#20714C211yesmaximal, characteristic
18C22×#125C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#484C2212yes—
23C2×#483C2212yes—
24C2×#479C2214yescomplemented
25C2×#431C2212yes—
26#2851—21no—
27#2851—21no—
28#2851—21no—
29#2851—21no—
30#2851C2212yes—
31#2851C2212yes—
32#2851C2212yes—
33#2851C2212yes—
34C4×C22⋊Q8—21no—
35C4×C22⋊Q8—21no—
36C4×C22⋊Q8—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8C2212yes—
39C4×C22⋊Q8C2212yes—
40C4×C22⋊Q8C2212yes—
41C4×C22⋊Q8C2212yes—
42C2×#391C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#387—21no—
47C2×#387—21no—
48C2×#387—21no—
49C2×#385—21no—
50C2×#385—21no—
51C2×#385—21no—
52C2×#382C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4—21no—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2085C2214yescomplemented
60#2077C2214yes—
61#2075C2214yes—
62#2074C2214yescomplemented
63#2059C2214yescomplemented
64#2036C2214yes—
65#2035C2214yes—
66#2026C2214yescomplemented
67#1989C2214yescomplemented
68#1949C2214yescomplemented
69#1942C2214yescomplemented
70#1941C2214yescomplemented
71#1933C2214yescomplemented
72#1933C2214yescomplemented
73#1921C2214yescomplemented
74#1919C2214yescomplemented
75#1872C2212yes—
76#1872C2212yes—
77#1865C2214yescomplemented
78#1863C2214yescomplemented
79#1853C2212yes—
80#1853C2212yes—
81#1853C2212yes—
82#1852C2212yes—
83#1852C2212yes—
84#1852C2212yes—
85#1824C2212yes—
86#1823C2212yes—
87#1823C2212yes—
88#1823C2212yes—
89#1817C2212yes—
90#1805C2214yescomplemented
91#1797C2212yes—
92#1797C2212yes—
93#1787C2212yes—
94#1787C2212yes—
95#1779C2211yescharacteristic
96#1779C2211yescharacteristic
97C4×C22⋊C8C2212yes—
98C4×C22⋊C8C2212yes—
99C23×Q8C2311yescharacteristic
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C2×#125—21no—
104C2×#125—21no—
105C2×#125—44no—
106C2×#125C2312yes—
107C2×#125C2312yes—
108C2×C22⋊Q8—21no—
109C2×C22⋊Q8—21no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8C2312yes—
112C2×C22⋊Q8C2312yes—
113C2×C4×Q8—21no—
114C2×C4×Q8—21no—
115C2×C4×Q8—44no—
116C2×C4×Q8C2312yes—
117C2×C4×Q8C2312yes—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C42—21no—
137C22×C42—21no—
138C22×C42—44no—
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#484—28no—
152#483—28no—
153#479—48no—
154#431—44no—
155C2×#107C2314yes—
156C2×#107C2314yes—
157C2×#106C2314yes—
158C2×#106C2314yes—
159C2×C4⋊C8C2314yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×C22⋊C8C2312yes—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2312yes—
169C2×C22⋊C8C2312yes—
170C2×C4×C8C2314yes—
171#391—21no—
172#391—21no—
173#391C2312yes—
174#391C2312yes—
175#389—21no—
176#389—21no—
177#389—21no—
178#389—21no—
179#389—21no—
180#389—21no—
181#389C2312yes—
182#389C2312yes—
183#389C2312yes—
184#389C2312yes—
185#389C2312yes—
186#389C2312yes—
187#387—22no—
188#387—22no—
189#387—22no—
190#387—22no—
191#387—22no—
192#387—22no—
193#387—22no—
194#387—22no—
195#387—22no—
196#387—22no—
197#387—22no—
198#387—22no—
199#385—22no—
200#385—22no—
201#385—22no—
202#385—22no—
203#385—22no—
204#385—22no—
205#385—22no—
206#385—22no—
207#385—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#382—21no—
212#382—21no—
213#382C2312yes—
214#382C2312yes—
215#380—21no—
216#380—21no—
217#380—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380C2312yes—
222#380C2312yes—
223#380C2312yes—
224#380C2312yes—
225#380C2312yes—
226#380C2312yes—
227C4×C4⋊C4—22no—
228C4×C4⋊C4—22no—
229C4×C4⋊C4—22no—
230C4×C4⋊C4—22no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4C2312yes—
234C4×C4⋊C4C2312yes—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C2×#95—21no—
240C2×#95—21no—
241C2×#95—21no—
242C2×#95—21no—
243C2×#95—21no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2314yes—
259#336C2314yes—
260C25C2×D411yescharacteristic
261C22×Q8—24no—
262C22×Q8—21no—
263C22×Q8—24no—
264C22×Q8—42no—
265C22×Q8C2412yes—
266C23×C4—24no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C22×C8C2414yes—
302C22×C8C2414yes—
303#125—28no—
304#125—44no—
305#125—44no—
306#125—44no—
307C22⋊Q8—28no—
308C22⋊Q8—28no—
309C22⋊Q8—24no—
310C22⋊Q8—24no—
311C22⋊Q8—24no—
312C22⋊Q8#4118yes—
313C4×Q8—28no—
314C4×Q8—44no—
315C4×Q8—44no—
316C4×Q8—44no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—44no—
388C2×C42—44no—
389C2×C42C2×D411yescharacteristic
390C2×C42C2×D411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2411yescharacteristic
402C2×C42C2411yescharacteristic
403C2×C42C2411yescharacteristic
404C2×C42C2411yescharacteristic
405#107—28no—
406#107—44no—
407#106—28no—
408#106—44no—
409C4⋊C8—28no—
410#103—28no—
411#103—28no—
412#103—44no—
413#103—44no—
414C22⋊C8—24no—
415C22⋊C8—24no—
416C22⋊C8—24no—
417C22⋊C8—24no—
418C22⋊C8—42no—
419C22⋊C8—42no—
420C4×C8—44no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—41no—
448C24—41no—
449C24#13514yes—
450C24C22×D411yescharacteristic
451C24C22×D411yescharacteristic
452C24C22×D411yescharacteristic
453C2×Q8—24no—
454C2×Q8—22no—
455C2×Q8—24no—
456C2×Q8—24no—
457C2×Q8—416no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8C2×#4114yes—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—416no—
523C22×C4—416no—
524C22×C4—416no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4#13714yes—
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C2×#4114yes—
560C22×C42−1+414yes—
561C22×C4C2511yescharacteristic
562C2×C8—24no—
563C2×C8—24no—
564C2×C8—24no—
565C2×C8—24no—
566C2×C8—24no—
567C2×C8—24no—
568C4⋊C4—24no—
569C4⋊C4—28no—
570C4⋊C4—28no—
571C4⋊C4—22no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—44no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4C2×#4114yes—
597C22⋊C4—28no—
598C22⋊C4—28no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—44no—
621C42—44no—
622C42—44no—
623C42—44no—
624C42H(5,𝔽2)14yes—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—28no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—28no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23#52512yes—
647C23#53612yes—
648C23C2×#13512yes—
649C23C2×#13512yes—
650C23C2×#13512yes—
651C23C2×#13712yes—
652C23#57512yes—
653C23C23×D411yescharacteristic
654Q8—28no—
655Q8—48no—
656Q8—44no—
657C2×C4—28no—
658C2×C4—28no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—48no—
702C2×C4—44no—
703C2×C4—48no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4#52512yes—
734C2×C4#53412yes—
735C2×C4#53412yes—
736C2×C4#53612yes—
737C2×C4C2×#13712yes—
738C2×C4C2×#13712yes—
739C2×C4#57512yes—
740C2×C4C22×#4112yes—
741C2×C4C2×H(5,𝔽2)12yes—
742C2×C4C2×2−1+412yes—
743C8—44no—
744C8—44no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—416no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22#310814yes—
766C22#323214yes—
767C22C2×#52511yescharacteristic
768C22C2×#53411yescharacteristic
769C22C2×#53611yescharacteristic
770C22C22×#13511yescharacteristic
771C22C22×#13711yescharacteristic
772C22C2×#57511yescharacteristic
773C22C2×#57511yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—22no—
781C4—41no—
782C4—44no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—44no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4#352014yes—
794C2—24no—
795C2—24no—
796C2—42no—
797C2#3508411yescharacteristic
798C2C2×#310811yescharacteristic
799C2#6056311yescharacteristic
800C2#6073411yescharacteristic
801C2#6075111yescharacteristic
802C2C2×#323211yescharacteristic
803C2#6086511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #33151C2semidirect
4. #32960C2semidirect
5. #30170C2semidirect
6. #29298C2semidirect
7. #29106C2semidirect
8. #27653C2semidirect
11. #24705C2semidirect
12. #24307C2semidirect
15. #22079C2semidirect
16. #22078C2semidirect
24. C2×#479C22semidirect
59. #2085C22semidirect
62. #2074C22semidirect
63. #2059C22semidirect
66. #2026C22semidirect
67. #1989C22semidirect
68. #1949C22semidirect
69. #1942C22semidirect
70. #1941C22semidirect
71. #1933C22semidirect
72. #1933C22semidirect
73. #1921C22semidirect
74. #1919C22semidirect
77. #1865C22semidirect
78. #1863C22semidirect
90. #1805C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#28512
C2×C4×C22⋊Q82
#331512
#329602
#301702
#292982
#291062
#276532
#276012
#276002
#247052
#243072
#240062
#240032
#220792
#220782
#207142